Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1189,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1189");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1189.6 | ||
Root | \(1.74361 + 1.00667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1189 |
Dual form | 3420.2.bj.c.2629.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0408382 | − | 2.23570i | −0.0182634 | − | 0.999833i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.34403i | − | 0.507994i | −0.967205 | − | 0.253997i | \(-0.918255\pi\) | ||
0.967205 | − | 0.253997i | \(-0.0817454\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.25594 | −1.58473 | −0.792363 | − | 0.610050i | \(-0.791149\pi\) | ||||
−0.792363 | + | 0.610050i | \(0.791149\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.10918 | + | 1.21773i | −0.584980 | + | 0.337738i | −0.763110 | − | 0.646269i | \(-0.776329\pi\) |
0.178130 | + | 0.984007i | \(0.442995\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.17765 | − | 0.679914i | −0.285621 | − | 0.164903i | 0.350344 | − | 0.936621i | \(-0.386065\pi\) |
−0.635965 | + | 0.771718i | \(0.719398\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89815 | + | 3.25587i | 0.664882 | + | 0.746949i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.05514 | − | 4.07329i | 1.47110 | − | 0.849339i | 0.471625 | − | 0.881799i | \(-0.343668\pi\) |
0.999473 | + | 0.0324603i | \(0.0103342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99666 | + | 0.182603i | −0.999333 | + | 0.0365207i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.03597 | + | 1.79435i | 0.192375 | + | 0.333203i | 0.946037 | − | 0.324059i | \(-0.105048\pi\) |
−0.753662 | + | 0.657262i | \(0.771714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.513207 | −0.0921747 | −0.0460873 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460873 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00483 | + | 0.0548876i | −0.507910 | + | 0.00927770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.57175i | − | 0.915991i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) | ||
0.888955 | − | 0.457995i | \(-0.151432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.70353 | + | 4.68265i | −0.422220 | + | 0.731307i | −0.996156 | − | 0.0875933i | \(-0.972082\pi\) |
0.573936 | + | 0.818900i | \(0.305416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0197 | − | 6.36221i | −1.68048 | − | 0.970228i | −0.961339 | − | 0.275369i | \(-0.911200\pi\) |
−0.719146 | − | 0.694859i | \(-0.755467\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82785 | + | 1.63266i | −0.412485 | + | 0.238148i | −0.691857 | − | 0.722035i | \(-0.743207\pi\) |
0.279372 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.19359 | 0.741942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.1892 | + | 5.88276i | −1.39960 | + | 0.808060i | −0.994351 | − | 0.106146i | \(-0.966149\pi\) |
−0.405250 | + | 0.914206i | \(0.632815\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.214643 | + | 11.7507i | 0.0289425 | + | 1.58446i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0175979 | + | 0.0304805i | −0.00229105 | + | 0.00396822i | −0.867169 | − | 0.498015i | \(-0.834063\pi\) |
0.864878 | + | 0.501983i | \(0.167396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.518372 | + | 0.897846i | 0.0663707 | + | 0.114957i | 0.897301 | − | 0.441419i | \(-0.145525\pi\) |
−0.830930 | + | 0.556376i | \(0.812191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.80861 | + | 4.66574i | 0.348366 | + | 0.578714i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.664028 | − | 0.383377i | 0.0811239 | − | 0.0468369i | −0.458889 | − | 0.888493i | \(-0.651753\pi\) |
0.540013 | + | 0.841657i | \(0.318419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.68450 | + | 9.84583i | −0.674625 | + | 1.16849i | 0.301953 | + | 0.953323i | \(0.402362\pi\) |
−0.976578 | + | 0.215163i | \(0.930972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.86429 | − | 1.07635i | −0.218199 | − | 0.125977i | 0.386917 | − | 0.922115i | \(-0.373540\pi\) |
−0.605116 | + | 0.796137i | \(0.706873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.06413i | 0.805032i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.48576 | + | 11.2337i | −0.729705 | + | 1.26389i | 0.227302 | + | 0.973824i | \(0.427009\pi\) |
−0.957008 | + | 0.290062i | \(0.906324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.20304i | 0.461343i | 0.973032 | + | 0.230672i | \(0.0740923\pi\) | ||||
−0.973032 | + | 0.230672i | \(0.925908\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.47199 | + | 2.66062i | −0.159660 | + | 0.288585i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65426 | + | 6.32937i | 0.387351 | + | 0.670912i | 0.992092 | − | 0.125510i | \(-0.0400568\pi\) |
−0.604741 | + | 0.796422i | \(0.706723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.63667 | + | 2.83479i | 0.171569 | + | 0.297166i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.16079 | − | 6.61235i | 0.734681 | − | 0.678413i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.721716 | + | 0.416683i | 0.0732791 | + | 0.0423077i | 0.536192 | − | 0.844096i | \(-0.319862\pi\) |
−0.462913 | + | 0.886404i | \(0.653196\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.40992 | + | 12.8344i | 0.737315 | + | 1.27707i | 0.953700 | + | 0.300759i | \(0.0972400\pi\) |
−0.216385 | + | 0.976308i | \(0.569427\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.40773i | 0.926971i | 0.886104 | + | 0.463486i | \(0.153401\pi\) | ||||
−0.886104 | + | 0.463486i | \(0.846599\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.8130i | − | 1.23868i | −0.785124 | − | 0.619338i | \(-0.787401\pi\) | ||
0.785124 | − | 0.619338i | \(-0.212599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.996875 | − | 1.72664i | 0.0954833 | − | 0.165382i | −0.814327 | − | 0.580406i | \(-0.802894\pi\) |
0.909810 | + | 0.415025i | \(0.136227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.34647i | 0.785170i | 0.919716 | + | 0.392585i | \(0.128419\pi\) | ||||
−0.919716 | + | 0.392585i | \(0.871581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.39474 | − | 15.6068i | −0.876064 | − | 1.45534i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.913823 | + | 1.58279i | −0.0837700 | + | 0.145094i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6249 | 1.51136 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.612300 | + | 11.1636i | 0.0547658 | + | 0.998499i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8240 | + | 10.2907i | −1.58163 | + | 0.913153i | −0.587005 | + | 0.809583i | \(0.699693\pi\) |
−0.994622 | + | 0.103569i | \(0.966974\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.36554 | − | 9.29339i | 0.468790 | − | 0.811967i | −0.530574 | − | 0.847639i | \(-0.678024\pi\) |
0.999364 | + | 0.0356712i | \(0.0113569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.37598 | − | 3.89519i | 0.379446 | − | 0.337756i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.8771 | − | 8.58931i | 1.27104 | − | 0.733834i | 0.295855 | − | 0.955233i | \(-0.404396\pi\) |
0.975183 | + | 0.221399i | \(0.0710622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.66394 | + | 6.34613i | 0.310771 | + | 0.538272i | 0.978530 | − | 0.206106i | \(-0.0660793\pi\) |
−0.667758 | + | 0.744378i | \(0.732746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.0857 | − | 6.40033i | 0.927033 | − | 0.535223i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.96932 | − | 2.38939i | 0.329634 | − | 0.198428i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.12292 | − | 10.6052i | 0.501609 | − | 0.868812i | −0.498389 | − | 0.866953i | \(-0.666075\pi\) |
0.999998 | − | 0.00185904i | \(-0.000591751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5577 | −0.940549 | −0.470274 | − | 0.882520i | \(-0.655845\pi\) | ||||
−0.470274 | + | 0.882520i | \(0.655845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0209584 | + | 1.14737i | 0.00168342 | + | 0.0921593i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58528 | + | 2.06996i | 0.286137 | + | 0.165201i | 0.636198 | − | 0.771526i | \(-0.280506\pi\) |
−0.350062 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.47460 | − | 9.48229i | −0.431459 | − | 0.747309i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.41672i | 0.737575i | 0.929514 | + | 0.368787i | \(0.120227\pi\) | ||||
−0.929514 | + | 0.368787i | \(0.879773\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.8395 | + | 6.83551i | −0.916164 | + | 0.528948i | −0.882409 | − | 0.470482i | \(-0.844080\pi\) |
−0.0337550 | + | 0.999430i | \(0.510747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.53425 | + | 6.12151i | −0.271866 | + | 0.470885i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1999 | + | 5.88891i | 0.775484 | + | 0.447726i | 0.834827 | − | 0.550512i | \(-0.185567\pi\) |
−0.0593437 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.245424 | + | 6.71565i | 0.0185523 | + | 0.507655i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.5727 | −1.23870 | −0.619350 | − | 0.785115i | \(-0.712604\pi\) | ||||
−0.619350 | + | 0.785115i | \(0.712604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.19552 | + | 12.4630i | 0.534839 | + | 0.926368i | 0.999171 | + | 0.0407069i | \(0.0129610\pi\) |
−0.464332 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.4567 | + | 0.227540i | −0.915838 | + | 0.0167291i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.18964 | + | 3.57359i | 0.452631 | + | 0.261327i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.97170 | 0.432097 | 0.216049 | − | 0.976383i | \(-0.430683\pi\) | ||||
0.216049 | + | 0.976383i | \(0.430683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1046 | + | 8.14331i | 1.01527 | + | 0.586168i | 0.912731 | − | 0.408560i | \(-0.133969\pi\) |
0.102542 | + | 0.994729i | \(0.467302\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.5233i | − | 0.820998i | −0.911861 | − | 0.410499i | \(-0.865355\pi\) | ||
0.911861 | − | 0.410499i | \(-0.134645\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.79943 | + | 8.31285i | 0.340222 | + | 0.589283i | 0.984474 | − | 0.175531i | \(-0.0561643\pi\) |
−0.644251 | + | 0.764814i | \(0.722831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.41166 | − | 1.39237i | 0.169265 | − | 0.0977253i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.5794 | + | 5.85303i | 0.738896 | + | 0.408794i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.2325 | − | 17.1127i | −1.05366 | − | 1.18371i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.28207 | − | 12.6129i | 0.501318 | − | 0.868308i | −0.498681 | − | 0.866786i | \(-0.666182\pi\) |
0.999999 | − | 0.00152265i | \(-0.000484675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.7739 | + | 24.8964i | −0.939375 | + | 1.69792i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.689764i | 0.0468242i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.31182 | 0.222777 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.55816 | − | 3.78635i | −0.439167 | − | 0.253553i | 0.264077 | − | 0.964501i | \(-0.414933\pi\) |
−0.703244 | + | 0.710949i | \(0.748266\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.86640i | − | 0.455739i | −0.973692 | − | 0.227869i | \(-0.926824\pi\) | ||
0.973692 | − | 0.227869i | \(-0.0731759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1011 | −1.46048 | −0.730240 | − | 0.683191i | \(-0.760592\pi\) | ||||
−0.730240 | + | 0.683191i | \(0.760592\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.57806 | − | 1.48844i | −0.168894 | − | 0.0975111i | 0.413170 | − | 0.910654i | \(-0.364421\pi\) |
−0.582064 | + | 0.813143i | \(0.697755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.76562 | + | 6.25555i | 0.245642 | + | 0.408067i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.71289 | −0.628275 | −0.314137 | − | 0.949378i | \(-0.601715\pi\) | ||||
−0.314137 | + | 0.949378i | \(0.601715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.34287 | + | 16.1823i | 0.601827 | + | 1.04239i | 0.992544 | + | 0.121884i | \(0.0388937\pi\) |
−0.390717 | + | 0.920511i | \(0.627773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.212097 | − | 11.6113i | −0.0135504 | − | 0.741818i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0775 | − | 3.33803i | −0.641216 | − | 0.212394i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.10091 | − | 3.63888i | −0.132608 | − | 0.229684i | 0.792073 | − | 0.610426i | \(-0.209002\pi\) |
−0.924681 | + | 0.380742i | \(0.875668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.0814 | + | 21.4090i | −2.33129 | + | 1.34597i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.3946 | + | 14.0842i | −1.52169 | + | 0.878548i | −0.522018 | + | 0.852934i | \(0.674821\pi\) |
−0.999672 | + | 0.0256140i | \(0.991846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.48859 | −0.465318 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.34563 | − | 1.35425i | −0.144637 | − | 0.0835065i | 0.425935 | − | 0.904754i | \(-0.359945\pi\) |
−0.570572 | + | 0.821247i | \(0.693279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.5682 | + | 22.5398i | 0.833486 | + | 1.38461i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.64101 | + | 9.77052i | −0.343938 | + | 0.595719i | −0.985160 | − | 0.171637i | \(-0.945094\pi\) |
0.641222 | + | 0.767356i | \(0.278428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.16690 | + | 5.48523i | −0.192375 | + | 0.333204i | −0.946037 | − | 0.324059i | \(-0.894952\pi\) |
0.753662 | + | 0.657263i | \(0.228286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.2622 | − | 0.959753i | 1.58367 | − | 0.0578753i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.1435i | − | 0.669549i | −0.942298 | − | 0.334774i | \(-0.891340\pi\) | ||
0.942298 | − | 0.334774i | \(-0.108660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9061 | + | 22.3541i | 0.769916 | + | 1.33353i | 0.937608 | + | 0.347694i | \(0.113035\pi\) |
−0.167693 | + | 0.985839i | \(0.553632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9942 | − | 14.4304i | −1.48575 | − | 0.857799i | −0.485883 | − | 0.874024i | \(-0.661502\pi\) |
−0.999868 | + | 0.0162249i | \(0.994835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.29360 | + | 3.63361i | 0.371500 | + | 0.214485i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.57543 | − | 13.1210i | −0.445614 | − | 0.771826i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.7742i | − | 1.33048i | −0.746628 | − | 0.665242i | \(-0.768328\pi\) | ||
0.746628 | − | 0.665242i | \(-0.231672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0688637 | + | 0.0380988i | 0.00400940 | + | 0.00221820i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.92035 | + | 17.1825i | −0.573709 | + | 0.993692i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.55098 | + | 14.8107i | −0.492870 | + | 0.853676i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.98614 | − | 1.19559i | 0.113726 | − | 0.0684592i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0275 | + | 8.09880i | 0.800593 | + | 0.462223i | 0.843679 | − | 0.536849i | \(-0.180385\pi\) |
−0.0430854 | + | 0.999071i | \(0.513719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.3483 | 1.60749 | 0.803743 | − | 0.594977i | \(-0.202839\pi\) | ||||
0.803743 | + | 0.594977i | \(0.202839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.67539 | − | 1.54464i | 0.151222 | − | 0.0873081i | −0.422480 | − | 0.906372i | \(-0.638840\pi\) |
0.573702 | + | 0.819064i | \(0.305507\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.8236 | + | 12.0225i | −1.16957 | + | 0.675251i | −0.953579 | − | 0.301144i | \(-0.902632\pi\) |
−0.215991 | + | 0.976395i | \(0.569298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.44500 | − | 9.43101i | −0.304861 | − | 0.528035i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.19928 | − | 5.80476i | −0.0667298 | − | 0.322986i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.3165 | − | 6.46975i | 0.572255 | − | 0.358877i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.19434 | + | 3.80071i | 0.120978 | + | 0.209540i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7717 | −1.14171 | −0.570857 | − | 0.821049i | \(-0.693389\pi\) | ||||
−0.570857 | + | 0.821049i | \(0.693389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.884231 | − | 1.46891i | −0.0483107 | − | 0.0802550i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.10139 | − | 1.21324i | −0.114470 | − | 0.0660892i | 0.441672 | − | 0.897177i | \(-0.354386\pi\) |
−0.556142 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.69739 | 0.146072 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.3885i | − | 0.884896i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.48834 | − | 1.43664i | −0.133581 | − | 0.0771230i | 0.431720 | − | 0.902008i | \(-0.357907\pi\) |
−0.565301 | + | 0.824885i | \(0.691240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.89385 | 0.315490 | 0.157745 | − | 0.987480i | \(-0.449578\pi\) | ||||
0.157745 | + | 0.987480i | \(0.449578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.0238i | − | 0.639962i | −0.947424 | − | 0.319981i | \(-0.896324\pi\) | ||
0.947424 | − | 0.319981i | \(-0.103676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.2444 | + | 12.3067i | 1.18061 | + | 0.653172i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.26590 | − | 3.92466i | 0.119590 | − | 0.207136i | −0.800015 | − | 0.599979i | \(-0.795175\pi\) |
0.919605 | + | 0.392844i | \(0.128509\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.20143 | + | 18.8720i | −0.115865 | + | 0.993265i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.33026 | + | 4.21195i | −0.121971 | + | 0.220463i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.9143 | − | 17.2710i | 1.56151 | − | 0.901539i | 0.564407 | − | 0.825496i | \(-0.309105\pi\) |
0.997105 | − | 0.0760429i | \(-0.0242286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.90659 | + | 13.6946i | 0.410490 | + | 0.710989i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 24.0801i | − | 1.24682i | −0.781894 | − | 0.623411i | \(-0.785746\pi\) | ||
0.781894 | − | 0.623411i | \(-0.214254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.37008 | − | 2.52307i | −0.225071 | − | 0.129945i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.1565 | −1.54904 | −0.774518 | − | 0.632552i | \(-0.782008\pi\) | ||||
−0.774518 | + | 0.632552i | \(0.782008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.6192 | − | 19.4101i | −1.71786 | − | 0.991809i | −0.922797 | − | 0.385286i | \(-0.874103\pi\) |
−0.795066 | − | 0.606522i | \(-0.792564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.7932 | − | 0.288486i | 0.804898 | − | 0.0147026i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6935 | − | 32.3781i | −0.947799 | − | 1.64164i | −0.750048 | − | 0.661383i | \(-0.769970\pi\) |
−0.197750 | − | 0.980252i | \(-0.563364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0779 | −0.560236 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.3799 | + | 14.0414i | 1.27700 | + | 0.706501i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4790 | − | 7.78211i | −0.676492 | − | 0.390573i | 0.122040 | − | 0.992525i | \(-0.461056\pi\) |
−0.798532 | + | 0.601952i | \(0.794390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3113 | − | 19.5918i | 0.564860 | − | 0.978366i | −0.432203 | − | 0.901777i | \(-0.642263\pi\) |
0.997063 | − | 0.0765898i | \(-0.0244032\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.08244 | − | 0.624949i | 0.0539203 | − | 0.0311309i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.2848i | 1.45159i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1239 | − | 31.3915i | −0.896169 | − | 1.55221i | −0.832351 | − | 0.554249i | \(-0.813005\pi\) |
−0.0638187 | − | 0.997962i | \(-0.520328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0409666 | + | 0.0236521i | 0.00201583 | + | 0.00116384i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.39671 | − | 0.171644i | 0.461266 | − | 0.00842569i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.5598 | −0.711293 | −0.355647 | − | 0.934621i | \(-0.615739\pi\) | ||||
−0.355647 | + | 0.934621i | \(0.615739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.784161 | + | 1.35821i | −0.0382177 | + | 0.0661950i | −0.884502 | − | 0.466537i | \(-0.845501\pi\) |
0.846284 | + | 0.532732i | \(0.178835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00846 | + | 3.18226i | 0.291453 | + | 0.154362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.20673 | − | 0.696705i | 0.0583977 | − | 0.0337159i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7303 | − | 22.0495i | −0.613197 | − | 1.06209i | −0.990698 | − | 0.136080i | \(-0.956550\pi\) |
0.377500 | − | 0.926009i | \(-0.376784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6212 | − | 8.44155i | 0.702650 | − | 0.405675i | −0.105684 | − | 0.994400i | \(-0.533703\pi\) |
0.808334 | + | 0.588725i | \(0.200370\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.7090 | + | 11.1656i | 1.61252 | + | 0.534125i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.93240 | − | 17.2034i | 0.474048 | − | 0.821075i | −0.525511 | − | 0.850787i | \(-0.676126\pi\) |
0.999558 | + | 0.0297121i | \(0.00945905\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.46422 | + | 2.57742i | −0.212101 | + | 0.122457i | −0.602288 | − | 0.798279i | \(-0.705744\pi\) |
0.390186 | + | 0.920736i | \(0.372411\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0013 | − | 8.42830i | 0.663726 | − | 0.399540i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2207 | −1.56778 | −0.783892 | − | 0.620897i | \(-0.786768\pi\) | ||||
−0.783892 | + | 0.620897i | \(0.786768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.2096 | − | 24.6117i | 0.669103 | − | 1.15892i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.27088 | − | 3.77485i | 0.293983 | − | 0.176968i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7126i | 0.547894i | 0.961745 | + | 0.273947i | \(0.0883293\pi\) | ||||
−0.961745 | + | 0.273947i | \(0.911671\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.68501 | + | 6.38263i | −0.171628 | + | 0.297269i | −0.938989 | − | 0.343947i | \(-0.888236\pi\) |
0.767361 | + | 0.641215i | \(0.221569\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8020i | 1.33854i | 0.743019 | + | 0.669271i | \(0.233393\pi\) | ||||
−0.743019 | + | 0.669271i | \(0.766607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 34.1251i | − | 1.57912i | −0.613673 | − | 0.789561i | \(-0.710309\pi\) | ||
0.613673 | − | 0.789561i | \(-0.289691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.515268 | − | 0.892471i | −0.0237929 | − | 0.0412105i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57.9188 | + | 33.4394i | 2.66311 | + | 1.53755i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0756 | − | 15.7393i | −0.691717 | − | 0.722169i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.4130 | − | 24.9640i | −0.658546 | − | 1.14064i | −0.980992 | − | 0.194048i | \(-0.937838\pi\) |
0.322446 | − | 0.946588i | \(-0.395495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.78491 | + | 11.7518i | 0.309365 | + | 0.535836i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.902102 | − | 1.63055i | 0.0409623 | − | 0.0740396i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5796i | 0.751294i | 0.926763 | + | 0.375647i | \(0.122579\pi\) | ||||
−0.926763 | + | 0.375647i | \(0.877421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.94615 | − | 8.56698i | 0.223217 | − | 0.386623i | −0.732566 | − | 0.680696i | \(-0.761678\pi\) |
0.955783 | + | 0.294073i | \(0.0950109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.81748i | − | 0.126893i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2331 | + | 7.64011i | 0.593584 | + | 0.342706i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.4949 | + | 26.8380i | −0.693649 | + | 1.20144i | 0.276985 | + | 0.960874i | \(0.410665\pi\) |
−0.970634 | + | 0.240561i | \(0.922669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.1406 | + | 6.43203i | −0.496735 | + | 0.286790i | −0.727364 | − | 0.686252i | \(-0.759255\pi\) |
0.230629 | + | 0.973042i | \(0.425922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.3911 | − | 17.0905i | 1.26339 | − | 0.760516i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.35312 | + | 12.7360i | 0.325921 | + | 0.564512i | 0.981698 | − | 0.190442i | \(-0.0609922\pi\) |
−0.655777 | + | 0.754955i | \(0.727659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.44664 | + | 2.50566i | −0.0639957 | + | 0.110844i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.0328 | − | 0.384195i | 0.926817 | − | 0.0169296i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.8630 | − | 8.58118i | 0.653676 | − | 0.377400i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.35528 | −0.234619 | −0.117310 | − | 0.993095i | \(-0.537427\pi\) | ||||
−0.117310 | + | 0.993095i | \(0.537427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.8388 | + | 7.98981i | −0.605127 | + | 0.349370i | −0.771056 | − | 0.636768i | \(-0.780271\pi\) |
0.165929 | + | 0.986138i | \(0.446938\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.604376 | + | 0.348937i | 0.0263270 | + | 0.0151999i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6833 | − | 37.5566i | 0.942753 | − | 1.63290i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13.1687i | − | 0.570400i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.6459 | + | 0.523258i | −1.23847 | + | 0.0226224i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.2972 | −1.17577 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9500 | − | 31.0904i | −0.771732 | − | 1.33668i | −0.936613 | − | 0.350366i | \(-0.886057\pi\) |
0.164881 | − | 0.986313i | \(-0.447276\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.90095 | − | 2.15820i | −0.167098 | − | 0.0924469i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6473 | + | 13.0754i | −0.968327 | + | 0.559064i | −0.898726 | − | 0.438511i | \(-0.855506\pi\) |
−0.0696011 | + | 0.997575i | \(0.522173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.83979 | + | 8.57329i | −0.120979 | + | 0.365235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0983 | + | 8.71704i | 0.642047 | + | 0.370686i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.64444 | − | 2.10412i | 0.154420 | − | 0.0891543i | −0.420799 | − | 0.907154i | \(-0.638250\pi\) |
0.575219 | + | 0.818000i | \(0.304917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.9899 | 1.31073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.5225i | 1.70782i | 0.520422 | + | 0.853909i | \(0.325775\pi\) | ||||
−0.520422 | + | 0.853909i | \(0.674225\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.6602 | − | 0.340855i | 0.785039 | − | 0.0143399i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.9522 | 1.00413 | 0.502064 | − | 0.864831i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864831i | \(0.332574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.78949 | −0.325980 | −0.162990 | − | 0.986628i | \(-0.552114\pi\) | ||||
−0.162990 | + | 0.986628i | \(0.552114\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.5084 | + | 21.6411i | −1.43910 | + | 0.902498i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.1385i | 1.42121i | 0.703593 | + | 0.710603i | \(0.251578\pi\) | ||||
−0.703593 | + | 0.710603i | \(0.748422\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.64899 | 0.234360 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53.5541 | − | 30.9195i | 2.21798 | − | 1.28055i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1737 | − | 11.0700i | −0.791384 | − | 0.456906i | 0.0490654 | − | 0.998796i | \(-0.484376\pi\) |
−0.840450 | + | 0.541890i | \(0.817709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.48735 | − | 1.67094i | −0.0612853 | − | 0.0688498i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.8131 | − | 20.6767i | 1.47067 | − | 0.849089i | 0.471208 | − | 0.882022i | \(-0.343818\pi\) |
0.999458 | + | 0.0329325i | \(0.0104846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.57595 | + | 1.97839i | 0.146600 | + | 0.0811061i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8243 | − | 29.1406i | −0.687423 | − | 1.19065i | −0.972669 | − | 0.232197i | \(-0.925409\pi\) |
0.285246 | − | 0.958454i | \(-0.407925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.4939 | 1.57020 | 0.785100 | − | 0.619369i | \(-0.212611\pi\) | ||||
0.785100 | + | 0.619369i | \(0.212611\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.678932 | − | 37.1683i | −0.0276025 | − | 1.51111i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.1827i | − | 0.900367i | −0.892936 | − | 0.450183i | \(-0.851359\pi\) | ||
0.892936 | − | 0.450183i | \(-0.148641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.97629 | − | 6.88714i | 0.160864 | − | 0.278624i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.13445 | + | 2.38703i | 0.166989 | + | 0.0964111i | 0.581165 | − | 0.813786i | \(-0.302597\pi\) |
−0.414176 | + | 0.910197i | \(0.635930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0178 | − | 8.09317i | 0.564335 | − | 0.325819i | −0.190549 | − | 0.981678i | \(-0.561027\pi\) |
0.754883 | + | 0.655859i | \(0.227693\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.4892 | −0.542176 | −0.271088 | − | 0.962555i | \(-0.587383\pi\) | ||||
−0.271088 | + | 0.962555i | \(0.587383\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.50684 | − | 4.91143i | 0.340819 | − | 0.196772i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9333 | − | 1.82482i | 0.997332 | − | 0.0729926i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.78832 | + | 6.56156i | −0.151050 | + | 0.261626i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.2207 | + | 22.8989i | 0.526308 | + | 0.911592i | 0.999530 | + | 0.0306488i | \(0.00975735\pi\) |
−0.473222 | + | 0.880943i | \(0.656909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.7348 | + | 39.4288i | 0.941886 | + | 1.56469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9542 | + | 6.32441i | −0.434021 | + | 0.250582i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.27817 | − | 7.41000i | 0.168977 | − | 0.292677i | −0.769083 | − | 0.639149i | \(-0.779287\pi\) |
0.938061 | + | 0.346471i | \(0.112620\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2681 | − | 14.0112i | −0.957042 | − | 0.552548i | −0.0617804 | − | 0.998090i | \(-0.519678\pi\) |
−0.895261 | + | 0.445541i | \(0.853011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.57376i | 0.376383i | 0.982132 | + | 0.188192i | \(0.0602626\pi\) | ||||
−0.982132 | + | 0.188192i | \(0.939737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0924936 | − | 0.160204i | 0.00363069 | − | 0.00628854i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.4168i | 0.642439i | 0.947005 | + | 0.321219i | \(0.104093\pi\) | ||||
−0.947005 | + | 0.321219i | \(0.895907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9963 | − | 11.6162i | −0.820394 | − | 0.453882i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.08162 | − | 12.2657i | −0.275861 | − | 0.477805i | 0.694491 | − | 0.719501i | \(-0.255629\pi\) |
−0.970352 | + | 0.241697i | \(0.922296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.5170 | − | 32.0724i | −0.720229 | − | 1.24747i | −0.960908 | − | 0.276868i | \(-0.910704\pi\) |
0.240679 | − | 0.970605i | \(-0.422630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.88717 | − | 9.62429i | −0.344630 | − | 0.373214i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6178 | + | 8.43960i | 0.566004 | + | 0.326783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.72453 | − | 4.71903i | −0.105179 | − | 0.182176i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.3293i | 1.63167i | 0.578282 | + | 0.815837i | \(0.303723\pi\) | ||||
−0.578282 | + | 0.815837i | \(0.696277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.9856i | 0.537510i | 0.963209 | + | 0.268755i | \(0.0866121\pi\) | ||||
−0.963209 | + | 0.268755i | \(0.913388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.560033 | − | 0.970005i | 0.0214921 | − | 0.0372254i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.6668i | 0.446416i | 0.974771 | + | 0.223208i | \(0.0716529\pi\) | ||||
−0.974771 | + | 0.223208i | \(0.928347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.8106 | − | 32.9099i | −0.756925 | − | 1.25742i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.3273 | − | 24.8156i | 0.545825 | − | 0.945397i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.7886 | −0.600627 | −0.300313 | − | 0.953841i | \(-0.597091\pi\) | ||||
−0.300313 | + | 0.953841i | \(0.597091\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0384 | − | 8.45062i | 0.532506 | − | 0.320550i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.36760 | − | 3.67633i | 0.241190 | − | 0.139251i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.64450 | + | 4.58042i | −0.0998816 | + | 0.173000i | −0.911635 | − | 0.411000i | \(-0.865180\pi\) |
0.811754 | + | 0.584000i | \(0.198513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.1409 | − | 16.1478i | 0.684198 | − | 0.609025i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.2497 | − | 9.95913i | 0.648743 | − | 0.374552i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2529 | − | 21.2226i | −0.460166 | − | 0.797031i | 0.538803 | − | 0.842432i | \(-0.318877\pi\) |
−0.998969 | + | 0.0454011i | \(0.985543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.62075 | + | 2.09044i | −0.135598 | + | 0.0782875i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.7619 | − | 24.5229i | −0.552064 | − | 0.917104i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.4239 | + | 38.8393i | −0.836269 | + | 1.44846i | 0.0567236 | + | 0.998390i | \(0.481935\pi\) |
−0.892993 | + | 0.450071i | \(0.851399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6442 | 0.470896 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.50405 | − | 8.77660i | −0.204415 | − | 0.325955i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.1376 | − | 16.2453i | −1.04357 | − | 0.602504i | −0.122726 | − | 0.992441i | \(-0.539164\pi\) |
−0.920842 | + | 0.389937i | \(0.872497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.65152 | + | 14.9849i | 0.319988 | + | 0.554235i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1969i | 0.413568i | 0.978387 | + | 0.206784i | \(0.0662998\pi\) | ||||
−0.978387 | + | 0.206784i | \(0.933700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.49009 | + | 2.01501i | −0.128559 | + | 0.0742237i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.466361 | − | 0.807761i | 0.0171554 | − | 0.0297140i | −0.857320 | − | 0.514783i | \(-0.827872\pi\) |
0.874476 | + | 0.485069i | \(0.161206\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.3370 | + | 13.4736i | 0.856153 | + | 0.494300i | 0.862722 | − | 0.505678i | \(-0.168758\pi\) |
−0.00656939 | + | 0.999978i | \(0.502091\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.9601 | − | 13.2559i | −0.877829 | − | 0.485658i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.2210 | −0.629240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.33645 | + | 4.04686i | 0.0852584 | + | 0.147672i | 0.905501 | − | 0.424343i | \(-0.139495\pi\) |
−0.820243 | + | 0.572015i | \(0.806162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.471994 | + | 25.8394i | 0.0171776 | + | 0.940392i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.0902 | + | 21.4140i | 1.34807 | + | 0.778306i | 0.987975 | − | 0.154612i | \(-0.0494126\pi\) |
0.360090 | + | 0.932918i | \(0.382746\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.7169 | 0.605987 | 0.302994 | − | 0.952993i | \(-0.402014\pi\) | ||||
0.302994 | + | 0.952993i | \(0.402014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.32065 | − | 1.33983i | −0.0840131 | − | 0.0485050i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.0857182i | − | 0.00309511i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.70852 | − | 13.3516i | −0.277976 | − | 0.481469i | 0.692905 | − | 0.721029i | \(-0.256330\pi\) |
−0.970882 | + | 0.239559i | \(0.922997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.7343 | + | 16.5897i | −1.03350 | + | 0.596691i | −0.917985 | − | 0.396615i | \(-0.870185\pi\) |
−0.115514 | + | 0.993306i | \(0.536852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.56432 | − | 0.0937133i | 0.0921132 | − | 0.00336628i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.0813 | + | 4.76868i | −0.826975 | + | 0.170856i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.8774 | − | 51.7491i | 1.06910 | − | 1.85173i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.48139 | − | 8.10014i | 0.159948 | − | 0.289106i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.8318i | − | 0.457405i | −0.973496 | − | 0.228702i | \(-0.926552\pi\) | ||
0.973496 | − | 0.228702i | \(-0.0734483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.2179 | 0.398862 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.18667 | − | 1.26248i | −0.0776511 | − | 0.0448319i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.28485i | 0.0809336i | 0.999181 | + | 0.0404668i | \(0.0128845\pi\) | ||||
−0.999181 | + | 0.0404668i | \(0.987115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.44028 | 0.157086 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.79861 | + | 5.65723i | 0.345786 | + | 0.199639i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.9759 | + | 12.6268i | −0.739305 | + | 0.445036i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.3304 | 0.609305 | 0.304652 | − | 0.952464i | \(-0.401460\pi\) | ||||
0.304652 | + | 0.952464i | \(0.401460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.7926 | − | 42.9420i | −0.870586 | − | 1.50790i | −0.861392 | − | 0.507941i | \(-0.830407\pi\) |
−0.00919378 | − | 0.999958i | \(-0.502927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0529 | − | 0.384562i | 0.737452 | − | 0.0134706i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.2221 | − | 54.3173i | −0.392612 | − | 1.90032i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1029 | + | 19.2308i | 0.387495 | + | 0.671160i | 0.992112 | − | 0.125356i | \(-0.0400073\pi\) |
−0.604617 | + | 0.796516i | \(0.706674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.5674 | + | 9.56519i | −0.577503 | + | 0.333422i | −0.760141 | − | 0.649759i | \(-0.774870\pi\) |
0.182637 | + | 0.983180i | \(0.441537\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0330 | + | 7.52461i | −0.453202 | + | 0.261656i | −0.709182 | − | 0.705026i | \(-0.750935\pi\) |
0.255980 | + | 0.966682i | \(0.417602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.62995 | −0.126074 | −0.0630368 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630368 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.11621 | − | 3.53120i | −0.211914 | − | 0.122349i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.7656 | + | 26.1903i | 0.545592 | + | 0.906351i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.47453 | − | 16.4104i | 0.327097 | − | 0.566549i | −0.654838 | − | 0.755770i | \(-0.727263\pi\) |
0.981935 | + | 0.189221i | \(0.0605963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3535 | − | 21.3969i | 0.425984 | − | 0.737826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.8302 | + | 7.65152i | 0.475772 | + | 0.263220i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.3443i | − | 0.767761i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.6954 | − | 39.3095i | −0.777987 | − | 1.34751i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.0287 | + | 21.3785i | 1.26784 | + | 0.731987i | 0.974579 | − | 0.224045i | \(-0.0719264\pi\) |
0.293260 | + | 0.956033i | \(0.405260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.71973 | + | 1.57024i | 0.0929043 | + | 0.0536383i | 0.545732 | − | 0.837960i | \(-0.316252\pi\) |
−0.452828 | + | 0.891598i | \(0.649585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.53437 | + | 6.12170i | 0.120591 | + | 0.208870i | 0.920001 | − | 0.391916i | \(-0.128188\pi\) |
−0.799410 | + | 0.600786i | \(0.794854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.464328i | − | 0.0158059i | −0.999969 | − | 0.00790296i | \(-0.997484\pi\) | ||
0.999969 | − | 0.00790296i | \(-0.00251562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7493 | − | 23.0443i | 0.433488 | − | 0.783531i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.0888 | − | 59.0435i | 1.15638 | − | 2.00291i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.933701 | + | 1.61722i | −0.0316373 | + | 0.0547973i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.0041 | − | 0.822948i | 0.507232 | − | 0.0278207i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.802896 | + | 0.463552i | 0.0271119 | + | 0.0156530i | 0.513495 | − | 0.858093i | \(-0.328351\pi\) |
−0.486383 | + | 0.873746i | \(0.661684\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.50850 | −0.151895 | −0.0759477 | − | 0.997112i | \(-0.524198\pi\) | ||||
−0.0759477 | + | 0.997112i | \(0.524198\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6605 | − | 17.1245i | 0.998156 | − | 0.576286i | 0.0904542 | − | 0.995901i | \(-0.471168\pi\) |
0.907702 | + | 0.419615i | \(0.137835\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.7321 | − | 14.2791i | 0.830423 | − | 0.479445i | −0.0235747 | − | 0.999722i | \(-0.507505\pi\) |
0.853997 | + | 0.520277i | \(0.174171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.8310 | + | 23.9560i | 0.463876 | + | 0.803457i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.5113 | − | 4.47544i | −0.452138 | − | 0.149765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.676798 | + | 37.0515i | 0.0226229 | + | 1.23849i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.531667 | − | 0.920874i | −0.0177321 | − | 0.0307129i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.9991 | 0.533007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.5696 | − | 16.5960i | 0.916445 | − | 0.551668i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6098 | + | 7.85765i | 0.451907 | + | 0.260909i | 0.708635 | − | 0.705575i | \(-0.249311\pi\) |
−0.256728 | + | 0.966484i | \(0.582644\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7125 | −0.686237 | −0.343119 | − | 0.939292i | \(-0.611483\pi\) | ||||
−0.343119 | + | 0.939292i | \(0.611483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 22.0909i | − | 0.731103i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.4906 | − | 7.21143i | −0.412475 | − | 0.238142i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.6628 | −1.01147 | −0.505737 | − | 0.862688i | \(-0.668779\pi\) | ||||
−0.505737 | + | 0.862688i | \(0.668779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 27.6888i | − | 0.911388i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.01742 | + | 27.8402i | 0.0334526 | + | 0.915380i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.65011 | − | 13.2504i | 0.250992 | − | 0.434731i | −0.712807 | − | 0.701360i | \(-0.752577\pi\) |
0.963799 | + | 0.266629i | \(0.0859099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.0518 | + | 16.9097i | 0.493303 | + | 0.554193i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.73669 | − | 13.9841i | 0.253017 | − | 0.457329i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.83862 | − | 2.21623i | 0.125402 | − | 0.0724011i | −0.435987 | − | 0.899953i | \(-0.643601\pi\) |
0.561389 | + | 0.827552i | \(0.310267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3400 | + | 30.0338i | 0.565268 | + | 0.979073i | 0.997025 | + | 0.0770825i | \(0.0245605\pi\) |
−0.431757 | + | 0.901990i | \(0.642106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.0490i | 1.43443i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.04606 | + | 0.603945i | 0.0339925 | + | 0.0196256i | 0.516900 | − | 0.856046i | \(-0.327086\pi\) |
−0.482907 | + | 0.875671i | \(0.660419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.24283 | 0.170189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.3773 | − | 29.6627i | −1.66427 | − | 0.960868i | −0.970639 | − | 0.240540i | \(-0.922676\pi\) |
−0.693633 | − | 0.720329i | \(-0.743991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.243873 | − | 13.3509i | −0.00789156 | − | 0.432025i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.5443 | − | 19.9952i | −0.372784 | − | 0.645680i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7366 | −0.991504 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.6300 | − | 31.8662i | 0.567528 | − | 1.02581i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.4450 | + | 22.7736i | 1.26847 | + | 0.732350i | 0.974698 | − | 0.223527i | \(-0.0717570\pi\) |
0.293769 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.738715 | − | 1.27949i | 0.0237065 | − | 0.0410608i | −0.853929 | − | 0.520390i | \(-0.825787\pi\) |
0.877635 | + | 0.479329i | \(0.159120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.52937 | − | 4.92443i | 0.273439 | − | 0.157870i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.8443i | 1.49868i | 0.662184 | + | 0.749341i | \(0.269630\pi\) | ||||
−0.662184 | + | 0.749341i | \(0.730370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.2066 | − | 33.2668i | −0.613846 | − | 1.06321i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.4012 | − | 10.0466i | −0.555011 | − | 0.320436i | 0.196130 | − | 0.980578i | \(-0.437163\pi\) |
−0.751141 | + | 0.660142i | \(0.770496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.7625 | + | 0.470589i | −0.820861 | + | 0.0149942i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −103.660 | −3.29621 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.95274 | + | 15.5066i | −0.284393 | + | 0.492583i | −0.972462 | − | 0.233062i | \(-0.925125\pi\) |
0.688069 | + | 0.725646i | \(0.258459\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.3890 | − | 11.0695i | 0.582971 | − | 0.350928i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.71445 | − | 0.989838i | 0.0542972 | − | 0.0313485i | −0.472606 | − | 0.881274i | \(-0.656686\pi\) |
0.526903 | + | 0.849926i | \(0.323353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3420.2.bj.c.1189.6 | 20 | ||
3.2 | odd | 2 | 380.2.r.a.49.8 | yes | 20 | ||
5.4 | even | 2 | inner | 3420.2.bj.c.1189.8 | 20 | ||
15.2 | even | 4 | 1900.2.i.g.201.8 | 20 | |||
15.8 | even | 4 | 1900.2.i.g.201.3 | 20 | |||
15.14 | odd | 2 | 380.2.r.a.49.3 | ✓ | 20 | ||
19.7 | even | 3 | inner | 3420.2.bj.c.2629.8 | 20 | ||
57.26 | odd | 6 | 380.2.r.a.349.3 | yes | 20 | ||
95.64 | even | 6 | inner | 3420.2.bj.c.2629.6 | 20 | ||
285.83 | even | 12 | 1900.2.i.g.501.3 | 20 | |||
285.197 | even | 12 | 1900.2.i.g.501.8 | 20 | |||
285.254 | odd | 6 | 380.2.r.a.349.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.3 | ✓ | 20 | 15.14 | odd | 2 | ||
380.2.r.a.49.8 | yes | 20 | 3.2 | odd | 2 | ||
380.2.r.a.349.3 | yes | 20 | 57.26 | odd | 6 | ||
380.2.r.a.349.8 | yes | 20 | 285.254 | odd | 6 | ||
1900.2.i.g.201.3 | 20 | 15.8 | even | 4 | |||
1900.2.i.g.201.8 | 20 | 15.2 | even | 4 | |||
1900.2.i.g.501.3 | 20 | 285.83 | even | 12 | |||
1900.2.i.g.501.8 | 20 | 285.197 | even | 12 | |||
3420.2.bj.c.1189.6 | 20 | 1.1 | even | 1 | trivial | ||
3420.2.bj.c.1189.8 | 20 | 5.4 | even | 2 | inner | ||
3420.2.bj.c.2629.6 | 20 | 95.64 | even | 6 | inner | ||
3420.2.bj.c.2629.8 | 20 | 19.7 | even | 3 | inner |